## Related questions with answers

Sketch the graph of a function that has the given properties. Identify any critical points, singular points, local maxima and minima, and inflection points. Assume that f is continuous and its derivatives exist everywhere unless the contrary is implied or explicitly stated. $f(-1)=0, f(0)=2, f(1)=1, f(2)=0, f(3)=1$, $\lim _{x \rightarrow \pm \infty}(f(x)+1-x)=0, f^{\prime}(x)>0 \text { on }(-\infty,-1)$, $(-1,0) \text { and }(2, \infty), f^{\prime}(x)<0 \text { on }(0,2)$, $\lim _{x \rightarrow-1} f^{\prime}(x)=\infty, f^{\prime \prime}(x)>0 \text { on }(-\infty,-1)$ and on (1, 3), and f"(x) < 0 on (-1, 1) and on $(3, \infty)$.

Solution

VerifiedFor this exercise, we are given a set of characteristics for a function that we are to sketch its graph. By sketching the graph, we are to also identify any critical points, singular points, extreme points, and inflection points.

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